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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ n$-representation-finite algebras and $ n$-APR tilting


Authors: Osamu Iyama and Steffen Oppermann
Journal: Trans. Amer. Math. Soc. 363 (2011), 6575-6614
MSC (2010): Primary 16G10, 16E35
Published electronically: July 11, 2011
MathSciNet review: 2833569
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Abstract: We introduce the notion of $ n$-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of $ n$-APR tilting and show that it preserves $ n$-representation-finiteness. We give some combinatorial description of this procedure and use this to completely describe a class of $ n$-representation-finite algebras called ``type A''.


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Additional Information

Osamu Iyama
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602 Japan
Email: iyama@math.nagoya-u.ac.jp

Steffen Oppermann
Affiliation: Institutt for Matematiske fag, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: steffen.oppermann@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05312-2
PII: S 0002-9947(2011)05312-2
Received by editor(s): September 3, 2009
Received by editor(s) in revised form: January 28, 2010
Published electronically: July 11, 2011
Additional Notes: The first author was supported by JSPS Grant-in-Aid for Scientific Research 21740010
The second author was supported by NFR Storforsk grant no. 167130.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.